Fixed Costs and Variable Costs

Posted by Professor Cram in Weblog

Dear Professor Cram:

Can you explain how to solve for fixed costs, variable costs, and total costs?

Renee, Bahamas

Thanks for your question, Renee.

Since I don't know how much you already know, let's start with some definitions.

  • Fixed costs are those costs which do not change as production or sales change within a relevant range.
  • Variable costs are directly proportional to sales or production volumes.
  • Mixed costs have components of both but can be divided into their fixed and variable components.

The challenge is identifying costs and determining whether they are fixed, variable, or mixed (and then splitting out the mixed into fixed and variable.)

By reviewing costs at two different production or sales levels, it is possible to determine the variable rates (just like finding the slope of a line in algebra.)

    Variable Costs = (cost per unit) X (number of units)
    Total Costs = (fixed costs) + (variable costs)

Here is a simplistic example to demonstrate the concept:

Bogus Manufacturing Company – selected data

  • Five sales reps are paid 5% commissions plus $500 monthly salary each
  • Utilities cost $1,000 per month plus $0.10 per unit manufactured
  • Materials cost is $0.75 per unit
  • Equipment cost $500,000 and has an expected life of 3,000,000 units with no salvage value
  • Rent is $10,000 per month
  • Other salaries are $20,000 per month

From these, we can identify the fixed and variable costs:

  • Five sales reps are paid 5% commissions plus $500 monthly salary each
      Fixed Costs = $500/month X 5 sales reps = $2,500 per month
      Variable Costs = 5% of sales
  • Utilities cost $1,000 per month plus $0.10 per unit manufactured
      Fixed Costs = $1,000 per month
      Variable Costs = $0.10 per unit produced
  • Materials cost is $0.75 per unit
      Variable Costs = $0.75 per unit produced (under GAAP this will go into inventory until sold and then show up in the Cost of Goods Sold – I am going to ignore that in this example and recognize the cost as we use the materials)
  • Equipment cost $50,000 and has an expected life of 3,000,000 units with no salvage value
      Depreciation here will be on units of production method at rate of $500,000/3,000,000 units = $0.1667 per unit in Variable Costs
  • Rent is $10,000 per month Fixed Costs
  • Other salaries are $20,000 per month Fixed Costs

Let's group the costs:

  • Fixed Costs
    • $ 2,500 per month for 5 sales reps
    • $ 1,000 per month Utilities
    • $ 10,000 per month Rent
    • + $20,000 per month Salaries
    • $33,500 per month Fixed Costs
  • Variable Costs
    • $ 0.05 per unit sales commissions (5%)
    • $ 0.75 per unit produced Materials
    • $ 0.10 per unit Utilities
    • + $0.1667 per unit Depreciation
    • $1.0167 per unit Variable Costs

Now that we have identified the cost components, let us solve for Total Cost. Let's expand the example data:

  • Manufacture and sell 100,000 units at a Selling Price of $3.50 per unit during one month
  • Fixed Costs are $33,500
  • Variable Costs are 5% of sales + $1.0167/unit

From this data, we can find variable costs (VC) and total costs (TC)

  • [Sales are $350,000 (100,000 units @ $3.50 each)]
  • VC = 5% X $350,000 + 100,000 X $1.01667
  • VC = $17,500 + $101,667 = $119,167
  • TC = FC + VC
  • TC = $33,500 + $119,167 = $152,667

From this, we know a lot of things. We can calculate their profit. We can even figure what sales are required to just break even called Break Even Point.

I hope this helps. Let us know if you need anything else.

Good Studying,

Professor Cram

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  1. Emmanuel Gbo-Musa says:

    a very simplistic lecture keep it up

  2. Syed Shaheruzzaman sajal says:

    It helps me very much.

  3. gaani says:

    thanks prof,,,just i can differentiate fixed cost and variable cost,,,,,,,,,

  4. darshina says:

    hello, i want the sollution of my sum.
    Mr H is considering the possibility of exporting his home brew to mainland UK from isle of barra.To determine the viability of the proect he has gathered the following budgeted annual information:
    selling price per bottle: £6.30
    destributers costs per 1000 bottels £600
    advertising & publicity £22,500
    Ingredients to make 1000 bottels £1600
    annual salary of shipping manager £21,000
    Duty due on each bottel £0.15
    Uk sales rep:annual salary £25000
    plus commission per bottel £0.25

    Required:
    A. Calculate the profit that would be earned if 30000 bottles were produced and sold.
    B. on the basis of the above information,how many must be sold to breakeven?
    C. Mr H was initially looking for a target profit of £25000 in the first year.How many bottels of home brew woul he therefore need to see?
    D. at the meeting to discuss the proect ,revised figures were considered.
    Advertising & publicity £21000
    Uk sales rep commition per bottle £0.30
    on the basis of this revised infermation ,how many bottels must be sold to achieve a revised profit target of £30,000?
    E. Disscuss why Mr.H would bother going through the budgeting process before launching his business.

    Please give me the solution of this question.

  5. Mishelly says:

    Hi! What is a different total variable cost per unit with variable cost per unit??
    Total variable cost per unit is mean more quantity more higher cost and
    variable cost per unit is mean less quantity less cost. Is it correct??

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